Game complete analysis of symmetric Cournot duopoly

Carfì, David and Perrone, Emanuele (2012): Game complete analysis of symmetric Cournot duopoly.

Abstract

In this paper we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in [3], [6], [8], [9], and already employed by himself and others in [4], [5], [7]) to the classic Cournot Duopoly (1838), classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ, as possible strategies, the quantities of the commodity produced. The main solutions proposed in literature for this kind of duopoly are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Cournot Duopoly as a differentiable game (a game with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Cournot game (this also in asymmetric cases with the help of computers) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.

• Item Type: MPRA Paper
• Language: English
• Keywords: duopoly; normal-form games; microeconomic Policy; complete study of differentiable games; bargaining solutions
• Subjects: B - History of Economic Thought, Methodology, and Heterodox Approaches > B2 - History of Economic Thought since 1925 > B21 - Microeconomics; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data ; Data Access; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O12 - Microeconomic Analyses of Economic Development; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Books

1. Aubin Jean Pierre, Mathematical Methods of Game and Economic Theory (Revised Edition), (North-Holland).

2. Aubin Jean Pierre, Optima and Equilibria, (Springer Verlag, 1998).

3. Carfì David, Topics in Game Theory, (Edizioni Il gabbiano, 2010).

Journal articles

4. Carfì David, Schilirò Daniele, Crisis in the Euro area: coopetitive game solutions as new policy tools, TPREF - Theoretical and Practical Research in Economic Fields, Summer issue 2011 http://mpra.ub.uni-muenchen.de/27138/

5. Carfì David, Ricciardello Angela, An algorithm for payoff space in C1 games, AAPP | Physical, Math-ematical, and Natural Sciences, Vol. LXXXVIII, issue 1, 2010 http://cab.unime.it/journals/index.php/AAPP/article/view/C1A1001003/

6. Carfì David, Differentiable game complete analysis for tourism firm decisions, Proceedings of THE 2009 INTER-NATIONAL CONFERENCE ON TOURISM and WORKSHOP on Sustainable tourism within High Risk areas of environmental crisis, Messina, April 22/25 (2009) http://mpra.ub.uni-muenchen.de/29193/

7. Carfì David, Globalization and Differentiable General Sum Games, Proceeding of 3rd International Symposium Globalization and convergence in economic thought, Faculty of Economics - Communication and Economic Doctrines Department - The Bucharest Academy of Economic Studies - Bucharest December 11/12 (2009)

8. Carfì David, Payoff space and Pareto boundaries of C1 Games, APPS vol. 2009 http://www.mathem.pub.ro/apps/v11/a11.htm

9. Carfì David, Complete study of linear infinite games, Proceedings of the International Geometry Center - Prooceeding of the International Conference “Geometry in Odessa 2009”, Odessa, 25 - 30 May 2009 - vol. 2 n. 3 (2009) http://proceedings.d-omega.org/

10. Carfì David, Optimal boundaries for decisions, Atti dell'Accademia Peloritana dei Pericolanti - Classe di Scienze Fisiche, Matematiche e Naturali Vol. LXXXVI, (2008) http://cab.unime.it/journals/index.php/AAPP/article/view/376

11. Carfì David, Ricciardello Angela, Non-reactive strategies in decision-form games, AAPP | Physical, Mathematical, and Natural Sciences, Vol. LXXXVII, issue 1, pp. 1-18 http://cab.unime.it/journals/index.php/AAPP/article/view/C1A0902002/0

12. Carfì David, Decision-form games, Proceedings of the IX SIMAI Congress, Rome, 22 - 26 September 2008, Communications to SIMAI congress, vol. 3, (2009) pp. 1-12 http://cab.unime.it/journals/index.php/congress/article/view/307

13. Carfì David, Reactivity in decision-form games, MPRA - paper 29001, University Library of Munich, Germany http://mpra.ub.uni-muenchen.de/29001/

14. Carfì David, Ricciardello Angela, Mixed Extensions of decision-form games, MPRA - paper 28971, University Library of Munich, Germany http://mpra.ub.uni-muenchen.de/28971/